Portfolio Greeks

Definition

Portfolio Greeks aggregate every option and stock position’s sensitivities into book-level numbers: net delta (direction), gamma (convexity), theta (time decay), and vega (volatility exposure). They answer the question no position-by-position view can: what does this BOOK do when the market moves, time passes, or volatility reprices — and they are the options book’s interface to portfolio risk management (port-exposure-netting consumes the delta; scenario analysis stress-tests what the Greeks linearize).

How it works / structure

• Aggregation rules (engine-executable): delta sums in delta-dollars per underlying then beta-nets across underlyings (index books sum cleanly; single-name books net only their common factor); GAMMA and VEGA sum per underlying but do NOT net safely across underlyings (short gamma in X and long gamma in Y is not flat — both tails are live); THETA sums in dollars/day with sign discipline (net theta states which side of the time-decay trade the book is on).
• The dispersion caveat: cross-underlying vega netting (short index vol vs long single-name vol or vice versa) is a CORRELATION position (the dispersion trade), not a hedge — the platform reports vega by underlying and by index-vs-single-name buckets separately.
• Surface dimensions: vega by expiry bucket (term structure exposure — opt-term-structure) and by strike region (skew exposure — opt-volatility-skew); a flat total vega can hide a steep calendar or skew position.
• The linearization boundary: Greeks are local derivatives — accurate for small moves; book-level decisions use scenario grids (full repricing at ±moves × vol shifts × days — risk-scenario-analysis), with the Greeks as the explanation layer (opt-second-order-greeks names the drift terms).

When it applies

Any book with more than one options position (single- position Greeks live in the position entries); hedging programs (mgmt-delta-hedging targets book delta); risk limits (books carry gamma/vega/theta limits alongside notional limits); expiry-week management (book gamma concentrates into expirations — event-opex, opt-0dte-mechanics).

Risk profile & failure modes

• Cross-underlying netting fiction: the signature aggregation error — netting gamma or vega across names reports a calm book that is actually long-and-short two different tails.
• Bucket-blind vega: total vega ≈ 0 with +vega in far months and −vega in front months is a term-structure position that a one-number report hides.
• Stale Greeks: book Greeks drift with spot, vol, and time (opt-second-order-greeks) — end-of-day Greeks on a short-dated book misstate morning risk; recomputation frequency is a risk parameter.
• Greeks-as-truth: model-derived numbers inherit model assumptions (opt-pricing-models) — smile-adjusted vs raw BSM Greeks differ materially on skewed books.

Evidence & limits

Aggregation mathematics is standard derivatives exposition (Hull); the OCC document is the mechanics authority. The netting caveats (cross-underlying, buckets) are structural mathematics, not opinions. Book-level Greek LIMITS are policy parameters the platform sets per book and audits against scenario losses — no universal thresholds are claimed.

Falsifiable-thesis examples

Illustrations only, not signals:

• “This book’s scenario P&L at a −3% index move will land within 1.5× its delta-gamma prediction (linearization audit)” — falsified by the repricing comparison.
• “Net theta will remain positive while book vega stays above −$10k/vol-point this month (premium-selling posture check)” — falsified by the daily Greek series.

Cross-references

• The components: greek-delta, greek-gamma, greek-theta, greek-vega, opt-second-order-greeks
• The surface dimensions: opt-term-structure, opt-volatility-skew
• The consumers: port-exposure-netting, mgmt-delta-hedging, risk-scenario-analysis
• The concentration dates: event-opex, opt-0dte-mechanics